Formation of electrostatic solitons, monotonic, and oscillatory shocks in pair-ion plasmas

Mahmood, S.; Ur‐Rehman, Hafeez

doi:10.1063/1.3458903

Cited by 41 publications

(23 citation statements)

References 27 publications

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“…the kink is always monotonic, and no oscillatory part nor peak or bell-shaped curve may appear in its graph, contrary to what is found in recent papers (Shah & Saeed 2009;Mahmood & Ur-Rehman 2010;Saeed & Shah 2010;Akhtar & Hussain 2011;Pakzad 2011a,b,c,d;Pakzad & Javidan 2011;Shah, Haque & Mahmoo 2011). There may be physical situations where shocks including oscillatory trails or precursors are observed, but these cannot be described by the KdVB formalism.…”

contrasting

confidence: 71%

“…As we will see, taking κ = 1 is not only needlessly stringent, but also erroneous, and in many cases one is not even able to verify that it holds, given the complexities in the expressions for A, B and C, except for specific numerical choice of all plasma parameters. Some other papers even leave κ undetermined, as if it were a free parameter (Mahmood & Ur-Rehman 2010;Akhtar & Hussain 2011).…”

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confidence: 99%

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Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Kourakis

Sultana

Verheest

2011

Astrophys Space Sci

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The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

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contrasting

confidence: 71%

mentioning

confidence: 99%

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Kourakis

Sultana

Verheest

2011

Astrophys Space Sci

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“…In this case, the exact solution of (32) can be constructed by means of different mathematical methods (Dutta et al 2012;El-Hanbaly 2003;El-Hanbaly and Abdou 2006;El-Wakil et al 2014;Mahmood and Ur-Rehman 2010). Among those, the tanh method has been proved to be a powerful mathematical technique for solving nonlinear partial differential equations (Malfliet and Hereman 1996).…”

Section: Kdv-burgers Equationmentioning

confidence: 99%

Effect of nonthermality fraction on dust acoustic growth rate in inhomogeneous viscous dusty plasmas

El-Shewy

El-Wakil

Elhanbaly

et al. 2014

Astrophys Space Sci

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The properties of linear dust acoustic (DA) waves in inhomogeneous viscous dusty plasmas with non-thermal electrons and ions have been investigated. A linear dispersion relation is obtained with the non-adiabatic dust charge fluctuation and fraction of nonthermality of electron-ion. The dependence of frequency and the damping rate of waves on the nonthermality fraction and dust kinematic viscosity coefficient are discussed. To study the dust acoustic shock waves, KdV-Burgers (KdV-B) equation for homogeneous dissipative dusty plasma has been considered and solved by means of tanh method. The obtained solution is a particular combination of a solitary wave with a Burgers shock wave. The present results are useful in the context of space plasma.

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“…In this case, the exact solution of equation (15) can be constructed by means of different mathematical methods (El-Hanbaly, 2003;El-Hanbaly & Abdou, 2006;Mahmood & Ur-Rehman, 2010;Dutta et al, 2012;El-Wakil et al, 2014b). Among those, the tanh method has been proved as a powerful mathematical technique for solving nonlinear partial differential equations.…”

Section: Stationary Solutionmentioning

confidence: 99%

Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

Elhanbaly¹,

El-Shewy²,

Kassem³

et al. 2016

APR

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The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained . The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

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Formation of electrostatic solitons, monotonic, and oscillatory shocks in pair-ion plasmas

Cited by 41 publications

References 27 publications

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Effect of nonthermality fraction on dust acoustic growth rate in inhomogeneous viscous dusty plasmas

Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

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